At present, there is no consensus on the most effective way to establish feature relevance for Gaussian process models. The most common heuristic, Automatic Relevance Determination, has several downsides; many alternate methods incur unacceptable computational costs. Existing methods based on sensitivity analysis of the posterior predictive distribution are promising, but are heavily biased and show room for improvement. This paper proposes Feature Collapsing as a novel method for performing GP feature relevance determination in an effective, unbiased, and computationally-inexpensive manner compared to existing algorithms.